1. Field of the Invention
The present invention generally relates to a method for allocating work in capacity planning and, more particularly, to a method for accurate capacity planning which deals with parallel, unrelated tools that can process the same operations at different rates and with the preferences for the sequence in which those tools are selected to accommodate the workload.
2. Background Description
The capacity of a manufacturing line is characterized by the tool set that occupies the line. This tool set may represent a large capital investment ($1B for semiconductor fabrication) and depreciation burden. It typically consists of multiple generations of tools giving rise to a mix of different equipment with different yields, availabilities and speeds for completing particular operations. Also, engineers typically have an understanding of which tools are best suited to perform a particular operation, which tools are next best, and so on. The best tool may be the fastest or highest yielding. The second best may be an older, slower, less reliable tool. Depending on the manufacturing environment and life cycles of the products and tools, there may be as many as five or more different tools that can perform a given process step, each with its own distinct operating characteristics.
Broadly speaking, manufacturing capacity planning addresses three kinds of problems:
(1) deciding the number of tools necessary to produce a particular product mix and volume;
(2) deciding what is the xe2x80x9coptimalxe2x80x9d product mix and volume to maximize the value of an existing tool set; and
(3) deciding on what additional tools to acquire to add to an existing tool set.
In a simple manufacturing environment, addressing all three questions is relatively straightforward. For example, for the case of calculating the required number of tools when operations are not shared among tools, one can simply divide the time required per day to perform all the operations done by a certain type of tool by the time available per day for this type of tool to arrive at an estimate of the number of required tools. However, in the more complex manufacturing environments in which different tools can perform the same or similar sets of operations, generally at different rates, these decisions become much more difficult because of the different ways in which work can be allocated among different tools. The necessity of respecting the preferred order in which the machines are assigned work further increases the level of the complexity of the problem.
Typically, capacity planning problems are addressed by making use of some type of mathematical model of the manufacturing process. The model may take the form of a simple spreadsheet, a detailed discrete event simulation, or a mathematical program such as a linear or mixed integer program. W. J. Hopp and M. L. Spearman, Factory Physics: Foundations of Manufacturing Management, Irwin (1996), and E. A. Silver and R. Peterson, Decision Systems for Inventory Management and Production Planning, 2nd Ed., John Wiley and Sons (1985), provide simple examples of conventional capacity planning problems and how to analyze them. W. Chou and J. Everton, xe2x80x9cCapacity Planning for Development Wafer Fab Expansionxe2x80x9d, Proc. of the 1997 7th Annual IEEE/SEMI Advanced Semiconductor Manufacturing Conference, pp. 17-22 (1996), describe the use of a discrete event simulation model in capacity planning. K. M. Bretthauer and M. J. Cote, xe2x80x9cNonlinear Programming for Multiperiod Capacity Planning in a Manufacturing Systemxe2x80x9d, European Journal of Operational Research, 96:1, pp. 167-179 (1997), and R. G. Kasilingam and C. Roze, xe2x80x9cFormulations of the Capacity Planning Problem Considering Manufacturing Flexibilityxe2x80x9d, International Journal of Systems Science, 27:10, pp. 1027-1031 (1996), describe mathematical programming models for capacity planning. L. M. Wein, xe2x80x9cCapacity Allocation in Generalized Jackson Networksxe2x80x9d, Operations Research Letters, Vol. 8. pp. 143-146 (1980), describes a method for capacity planning based on a queuing network model that assumes, among other things, that all tools capable of performing a given operation are identical. R. C. Leachman and T. F. Carmon, xe2x80x9cOn Capacity Modeling for Production Planning with Alternative Machine Typesxe2x80x9d, IIE Transactions, 24:4, pp. 62-72 (1992), discuss capacity modeling with alternate machine types, but present a method that assumes that processing times among such alternate machine types are identical or proportional across operations they can perform. None of the above addresses capacity planning problems in which work can be allocated to different tools, with varying ratios of process times from operation to operation and in which there exists a preferred order in which tools are used.
It is therefore an object of the invention to provide a method for accurate capacity planning which deals with parallel, unrelated tools that can process the same operations at different rates and with the preferences for the sequence in which those tools are selected to accommodate the workload.
It is another object of the invention to provide a method for the reliable determination of precisely what are the gating (bottleneck) tools among sets of parallel, unrelated tools in a complex manufacturing environment in which different tools can perform the same or similar sets of operations, generally at different rates.
According to the invention, there is provided a method implemented on a computation engine that aggregates very raw data detailing by time period, the processing times, tool availabilities, load factors, and the number of passes per product for every operation on every tool group in the manufacturing line into the required inputs. The computation engine scans the list of operations, locating identical operation names within cascade sets of tool groups and organizes tool groups and the operations into the appropriate cascade groups. The primary, secondary, etc. tool groups in each cascade set are explicitly kept track of in order to enable the correct penalty function to be associated with the appropriate tool group. The end user may also interact with the input data through a Menu Program or through a Graphical User Interface (GUI) and modify the data (for example, changing the allowed ranges for product starts, the profits associated with each product and/or the numbers of tools per tool group) for xe2x80x9cwhat-ifxe2x80x9d analyses.
The method according to the invention for allocating work in rank order across parallel unrelated tools for capacity planning is formulated as a non-integer, linear program with piecewise-linear penalty terms incorporated into the objective function which serve to discourage, but not prevent, using a tool group to greater than 100% of its available time and to distribute work in the preferred sequence among such parallel, unrelated tool groups. In this way, the implementation is able to provide output data on both the number of tools needed for a particular product mix and volumes and on the optimal product mix and volumes for a fixed tool set. Output data is contained in formatted output reports by individual time period and in multi-period summary reports which detail required versus available numbers of tools and/or the derived optimum number of starts per day by product.
The results of the various xe2x80x9cwhat-ifxe2x80x9d scenarios are organized into sets of files whose filenames end in a characteristic suffix, a trial name, initially selectable by the user and which he can use to retrieve such files by selection through the GUI or Menu. If desired, detailed output reports can be printed breaking down tool group usage by operation, such information frequently being of vital interest to engineers with responsibility for particular cascade sets.
The implementation also includes a module, that using the capability described in the invention of being able to identify truly gating tool groups among parallel, unrelated tool groups, selects those tool groups for incrementing, producing a new optimal solution for product mix and volume that represents the most efficient way of increasing manufacturing line output for the least number of additional tools. Any number of automatic iterations of the tool set can be set by the user.